Numerical Weather prediction models have improved drastically in the last few decades with advances in data assimilation, improved parameterization, and ensemble forecasting. Despite these developments, the performance of numerical weather prediction models like the Global Forecast System (GFS) is still limited by errors in the model forecasts. These errors arise from inaccuracies in the initial condition and model’s inability to accurately represent physics, dynamics, and chemical processes. Operation centers generally use an offline correction scheme that corrects the forecast error after the forecast is generated. Past research has shown that another class of correction schemes, the online correction schemes that correct for the forecast errors during the model integration have certain advantages over offline schemes. However, the online schemes tested so far are prohibitive for operation use. The goal of this work is to introduce and test an ``adaptive online correction scheme” based on the methodology developed by (Danforth et al., 2007) that is suitable for operational use is introduced and implemented.

As a first step towards correcting the tendency equation, the model errors are estimated using the 6-hr Analysis Increments (AIs). Assuming initial linear error growth and absence of observation bias in the analysis, 6-hr AIs provide a measure of model errors that can later be used to estimate model tendency errors. Seasonal means of 6-hr AIs during the period from 2012-2016 indicate robust model biases despite the changes in the model and data assimilation during that period. Apart from the season means, GFS also has significant periodic errors that are dominated by errors in the diurnal and semi-diurnal cycle.

An adaptive online correcting scheme that uses 6-hr AIs, averaged over a moving training period to compute the bias correction term to be added in the model integration equation is then implemented with GFS. The scheme is tested using training periods of different lengths ranging from past 7 to 28 days. This scheme is remarkably stable and reduces the forecasts errors significantly in forecasts all over the globe at lead times of 1 day and shorter and over the tropics at longer lead times. An offline correction scheme was also tested but found to be less effective than the online correction scheme especially at lead times longer than 1-day.